Question

1. $6x^2 + 7x - 2$7. $2x^2 - 5x + 3$

Explanation:

Problem 4: $6x^2 + 7x - 20$

Step1: Find factor pairs

Multiply $6\times(-20)=-120$. Find two numbers that multiply to $-120$ and add to $7$: $15$ and $-8$.

Step2: Split middle term

Rewrite $7x$ as $15x-8x$:
$6x^2 + 15x - 8x - 20$

Step3: Factor by grouping

Group terms: $(6x^2 + 15x) + (-8x - 20)$
Factor out GCFs: $3x(2x + 5) - 4(2x + 5)$
Factor common binomial: $(3x - 4)(2x + 5)$

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Problem 7: $2x^2 - 5x + 3$

Step1: Find factor pairs

Multiply $2\times3=6$. Find two numbers that multiply to $6$ and add to $-5$: $-2$ and $-3$.

Step2: Split middle term

Rewrite $-5x$ as $-2x-3x$:
$2x^2 - 2x - 3x + 3$

Step3: Factor by grouping

Group terms: $(2x^2 - 2x) + (-3x + 3)$
Factor out GCFs: $2x(x - 1) - 3(x - 1)$
Factor common binomial: $(2x - 3)(x - 1)$

Answer:

1. $(3x - 4)(2x + 5)$
2. $(2x - 3)(x - 1)$